Question: Solve for $x$ and $y$ using elimination. ${2x-5y = -36}$ ${2x-3y = -20}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-2x+5y = 36}$ $2x-3y = -20$ Add the top and bottom equations together. $2y = 16$ $\dfrac{2y}{{2}} = \dfrac{16}{{2}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {2x-5y = -36}\thinspace$ to find $x$ ${2x - 5}{(8)}{= -36}$ $2x-40 = -36$ $2x-40{+40} = -36{+40}$ $2x = 4$ $\dfrac{2x}{{2}} = \dfrac{4}{{2}}$ ${x = 2}$ You can also plug ${y = 8}$ into $\thinspace {2x-3y = -20}\thinspace$ and get the same answer for $x$ : ${2x - 3}{(8)}{= -20}$ ${x = 2}$